Things like the shuttlecraft mockup are borderline objects, sort of like driving a car onto a set. Not exactly a prop, but neither is it a set.
But in your example, that car would be a prop. Another car seen only in the background parked on a street would be set dressing-- unless an actor drives off with it, then it qualifies as a prop. Both would come under the property master's jurisdiction, probably in collaboration with the transportation captain.
It's so confusing, we should just wait for a member of the union to step in here to put it straight.